Results 11 to 20 of about 74,199 (261)

The local limit theorem of Delange in the Knopfmacher's semigroup

Lietuvos Matematikos Rinkinys, 2004
An asymptotic formula of the mean value of multiplicative arithmetic function from the class Ma(G)  with asymptotical expansion of the main term is obtained. In the present paper the local limit theorem of the H. Delange type is proved.
Rimantas Skrabutėnas
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ON A SUM INVOLVING CERTAIN ARITHMETIC FUNCTIONS ON PIATETSKI–SHAPIRO AND BEATTY SEQUENCES

Проблемы анализа, 2022
Let 𝑐, 𝛼, 𝛽 ∈ R be such that ...
T. Srichan
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Asymptotical expansions in the Kubilius theorem of large deviations

Lietuvos Matematikos Rinkinys, 2005
In the present paper, a local theorem of large deviations for arithmetic functions defined in Knopfmacher’s semigroup is obtained.
Rimantas Skrabutėnas
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New properties of arithmetic functions related to gcd and lcm [PDF]

Notes on Number Theory and Discrete Mathematics
This paper explores additional properties of the arithmetic functions f_α(n) and g_α(n), defined respectively by f_α(n)=Πʳᵢ₌₁pᵢ^{(eᵢ,α)} and g_α(n)=Πʳᵢ₌₁pᵢ^{[eᵢ,α]}, where n=Πʳᵢ₌₁pᵢ^eᵢ is the prime factorization of a positive integer n>1, (a,b) and [a,b]
Brahim Mittou
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New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility

Axioms, 2023
The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms.
Hsien-Chung Wu
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On a certain class of arithmetic functions [PDF]

Mathematica Bohemica, 2017
A homothetic arithmetic function of ratio $K$ is a function $f \mathbb{N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in\mathbb{N}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general.
Antonio M. Oller-Marcén
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Multidimensional local theorem in the Knopfmachers semigroup

Lietuvos Matematikos Rinkinys, 2007
In the presentpaper a multidimensionallocal theorem for arithmetic functions definedin the Knopfmachers semigroup G is obtained.
Rimantas Skrabutėnas
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The mean value of the function d(n)/d*(n) in arithmetic progressions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
Let d(n) and d*(n) be, respectively, the number of divisors and the number of unitary divisors of an integer n≥1. A divisor d of an integer is to be said unitary if it is prime over n/d.
Ouarda Bouakkaz, Abdallah Derbal
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Exponential sums involving the divisor function over arithmetic progressions

AIMS Mathematics, 2023
Let $ \phi(x) $ be a smooth function supported on $ [1, 2] $ with derivatives bounded by $ \phi^{(j)}(x)\ll 1 $ and $ d_3(n) $ be the number of ways to write $ n $ as a product of three factors. We get the asymptotic formula for the nonlinear exponential
Rui Zhang , Yang Li, Xiaofei Yan
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Further Results on a Curious Arithmetic Function

Journal of Mathematics, 2020
Let p be an odd prime number and n be a positive integer. Let vpn, N∗, and Q+ denote the p-adic valuation of the integer n, the set of positive integers, and the set of positive rational numbers, respectively.
Long Chen, Kaimin Cheng, Tingting Wang
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